It's clear from Genesis 2 and 3 that life in Eden was simple (2:15) and innocent (2:24). We know that Adam didn't have to work for his bread (3:19) and that Eve had no pain in childbirth (3:16). However, should we also assume that life in Eden precluded any unpleasant experiences or that life in Eden was characterized by ceaseless pleasure? Was there death in Eden before the fall? What is the implication of verse 3:22 in that regard?

3 Answers
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From Genesis

It seems the man (and woman) had not gained anything like immortality yet according to Genesis 3:22. I'm re-quoting from the NJPS since it's more understandable:

And the Lord God said, “Now that the man has become like one of us, knowing good and bad, what if he should stretch out his hand and take also from the tree of life and eat, and live forever!”

Whether or not anything died or suffered up to that point is not known. The text of the curse implies that various hardships were not known to Adam and Eve, but it's possible the text means that these were not present in Eden. It's possible they always existed outside of Eden and the way the curse was implemented was verses 23-24:

So the Lord God banished him from the garden of Eden, to till the soil from which he was taken. He drove the man out, and stationed east of the garden of Eden the cherubim and the fiery ever-turning sword, to guard the way to the tree of life.

And God saw all that He had made, and found it very good. And there was evening and there was morning, the sixth day.

Thematically it seems like "very good" in this context means without the suffering and pain implied in the curse of found in chapter 3. But it could be that "very good" means that everything God made was well ordered and in it's proper place. If so, there might be pain and suffering, but they would be serving their proper function.

A Philosophical Aside

There's a philosophical question of whether good and evil are opposite sides of the same concept or whether they are distinct ideas which is raised here. What actually happens when "evil" enters a world? If Evil is an entity opposing Good, then it's entirely possible that pain, suffering and death entered into the world at the moment of the fall. On the other hand, if evil is not an opposing entity, but is merely the absence of good, then pain, suffering and death would always have been potentially part of creation. At the moment of the fall, these unpleasant events would start to have negative effects on creation.

An analogy might be to imagine creation before the fall as a perfectly designed Porsche 911 (or perhaps a Toyota Hilux). In the dualist view, God is the driver and Satan gets into the passenger seat and starts interfering with God: pulling at the steering wheel, moving the rear-view mirror, trying to set the parking break, and so on. But the neoplatonic view is that when the fall occurred, creation was broken. It's as if someone pulled a random hose so that the car keeps running, but not well. In the first model, something new and separate from creation causes problems and in the second, these things were always latent in creation until they were activated by the fall.

If we knew for sure which of these models Genesis had in mind, we could make more educated guesses about whether "unpleasant" things such as death, pain and suffering were possible or actual or neither before the fall. But since we see elements of each view, we can't.

A Christian Perspective

Normally I prefer to answer Tanakh questions from the text itself and not rely on Christian sources. But in this case, the answer is too good to pass up. According to the John's vision of the end of this age, the end point of history will be a state without pain, suffering or death:

Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and the sea was no more. And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. And I heard a loud voice from the throne saying, “Behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God. He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away.”—Revelation 21:1-4 ESV)

The suggestion here is that the new heaven and new earth will replace the current heaven and earth, which are full of death and pain. Strongly implied by this vision is that the new existence will fulfill the promise of the original creation. Therefore, God's intention before the fall was that there would be no death, pain or suffering.

Summary

Genesis does not say for sure that there was no death or pain before the fall, but it seems to be strongly implied that there was not. Certainly God withheld the fruit of the tree of life (which would allow man to live forever) from Adam because he ate fruit forbidden to him.

Nice answer, +1. According to your answer "And God saw all that He made, and found it very good," doesn't apply to the world as we find it today. I find this assumption to be very difficult to accept and I think there is strong literary/thematic/textual evidence to the contrary. Moreover, I don't think Genesis 1 is talking or can be applied to the Garden of Eden at all. Perhaps we'll get a chance to discuss this issue in chat sometime.
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AmichaiDec 13 '11 at 3:58

@Amichai: I struggle with this question as well and I hope my update shows that it's not easy to solve and philosophical preconceptions have a role in determining which answer we might chose. I guess I would say that the world we find today is good, but not very good because humanity is failing in our mission after the fall. But there's no doubt my thinking on this is entirely informed by Paul of Tarsus.
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Jon Ericson♦Dec 14 '11 at 0:56

I think life in the garden before the fall would have been like life after the fall, but having the knowledge of good and evil - blessing and calamity, being separated from God (born into sin; having natural enmity towards Him), and being under the listed curses. It depends on what you mean by "unpleasant experiences", but I'm sure they felt pain when they stubbed their toe, got fatigued, etc. As far as ceaseless pleasures, they weren't yet separated from God and so they probably didn't have the desire to over indulge in the Lord's creations, but enjoy them modestly.

I think it is also possible that they had eternal life, as God said they would surely die from eating the fruit, and in one of the curses God says "In the sweat of your face shall you eat bread until you return to the ground, for out of it you were taken; for dust you are and to dust you shall return." (Gen 3:19). They were not instructed to not eat of the tree of life, maybe because they already had eternal life. But once God placed these curses, he had taken that away from them and removed them from the garden lest they eat it after the fall.

As in many places, the Old Testament is much clarified by the commentaries of New Testament writers. According to Paul in Romans 5:12-14, death came through the sin of Adam. And in chapter 8 it becomes clear that this is as a result of a curse that applies to all the creation. Moreover, to maintain the comparison Paul is making between the destruction that has come through Adam and the blessing that comes through Christ, it is necessary to properly emphasize the glory of the prelapsarian state (see also 1 Corinthians 15:21-22). For more on whether they were in ceaseless bliss, it would be necessary to make an in-depth study of the theology of how Adam walked with God before the fall.